Traditional implementations of floating-point convergent division algorithms and square root algorithm determinations are hampered by the lack of efficient computation of convergence factors within both algorithms. Convergence algorithms utilize repeated multiplication to achieve results of a predetermined accuracy. A feasible range of a modified input value, X, has been shown to be 0&lt;X&lt;2. Further limitation of such a range would expedite algorithmic determinations.
In addition, determination of a convergence factor for convergent division generally requires a normalization step, a subtraction operation requiring a carry-propagate step, and another normalization step. Determination of a convergence factor for a square root computation, in addition, requires a scaling computation. Evaluation of a convergence factor for both the convergent division and the square root determination thus requires more computation cycles than a floating-point multiplication computation. Because the convergence factors occur serially in both computations, the inefficiency of the computation of the convergence factors has directly reduced the efficiency of computation within both the convergent division and square root determination algorithms.
The need exists for a more efficient method of determining convergence factors for convergent division and for square root determination to facilitate these two over-all processes within a digital platform.